If the lines 2x + 3y = 5 and kx - 6y = 7 are parallel, then the value of k is

1. 4

2. -4

3. $\dfrac{1}{4}$

4. -$\dfrac{1}{4}$

Given,

⇒ 2x + 3y = 5 and kx - 6y = 7

⇒ 3y = -2x + 5 and 6y = kx - 7

⇒ y = $-\dfrac{2}{3}x + \dfrac{5}{3}$ and y = $\dfrac{k}{6}x - \dfrac{7}{6}$

Comparing both the equations with y = mx + c,

Slope of first line = m₁ = $-\dfrac{2}{3}$

Slope of second line = m₂ = $\dfrac{k}{6}$

Since, both the lines are parallel so,

m₁ = m₂

$\Rightarrow -\dfrac{2}{3} = \dfrac{k}{6} \\[1em] \Rightarrow k = -\dfrac{2}{3} \times 6 \\[1em] \Rightarrow k = -4.$

Hence, Option 2 is the correct option.